Wash potato and stab it with a fork several times to create air holes. Wrap the potato in a paper towel and microwave on high for five minutes. Allow the potato a few minutes to cool before handling. It's easier to handle the potato while wearing disposable gloves.
Next, using your knife and fingers, peel off and discard the potato skin. Finely grate the potato into small pieces. You'll wind up with about 1.5 cups of grated potatoes.
Combine potatoes with pumpkin and mix well with your hands. Add egg, flour and salt and continue mixing by hand.
Divide dough into about 6 small sections. Roll out each section into a long snake and then cut dough into small bite-sized pieces with your knife. Add gnocchi to a plate coated with a little flour to keep them from sticking to one another.
Bring a pot of water to a boil and cook gnocchi in two batches. Once a gnocchi floats to the top of the water (about 1 minute), use a slotted spoon to remove it from the water and set it aside in a bowl.
Heat 2 Tbsp butter in a large non-stick saucepan. Add gnocchi and allow it to cook, undisturbed, for two minutes before mixing. Continue to cook gnocchi on all sides for about 6-8 minutes. Remove gnocchi from saucepan and set aside in a bowl.
Heat another 2 Tbsp. butter in a large saucepan. Add garlic and sage and cook for 30 seconds. Add chicken broth and bring mixture to a boil.
In a small bowl, combine 1 Tbsp. flour with 2 Tbsp. water to create a slurry. Mix well. While whisking the chicken broth mixture, add the slurry to the sauce and continue whisking until mixture thickens, about one minute.
Add gnocchi to saucepan and coat with sauce. Serve immediately.